FIG. 13 is a block diagram showing the flow of a servo system control signal in a conventional position control system by using transfer functions. Referring to the Figure, designated at 1 is a position loop gain operational unit having a gain Kp, at 2 a speed loop proportional integral compensation unit, at 3 an inertia unit, and at 4 an integrator. In FIG. 13, a position feedback signal is subtracted from a position command at point A, and the difference is amplified in the position loop gain operational unit 1, which has a transfer function kp and outputs a speed command. From the speed command, a speed feedback signal is subtracted at point B, and the difference is amplified in the speed loop proportional integral compensation unit 2, which has a transfer function Kv+Ki/S and outputs a torque command. The torque command represents the motor speed corresponding to the inertia component, less a reduction corresponding to a load torque, as seen at point C. The speed is negatively fed back from point D as the speed feedback signal as noted above. The position value, which is the time integral of the speed, is taken out at point E from the integrator 4, which has a transfer function 1/S and generates the position feedback signal.
When a machine is actually operated in the above system, the operation of the machine is equivalently approximated by the position loop response as shown in FIGS. 14A, 14B because the position loop response is sufficiently high compared to the speed loop response. The characteristic of the position loop shown in FIG. 14A is given as a transfer function G (S) ##EQU1##
Next a description is made for FIG. 14B. When a positional command for moving to a specified position at a timing to (migration length S) is given, actual movement of a machine (motor) follows with a follow-up delay of the positional loop (by the positional loop time constant). A speed command for the position at this point of time is inputted as shown in the figure, and this area provides the specified position (time.times.speed). When the input as described above is provided, a rotation of the motor is executed with a time-lag of the first order, as shown in the figure. Also, the motor generates a steep torque when acceleration is started and when deceleration is started.
In the above position control system, the position loop has a first degree delay time constant and follows the command. Thus, with a real circle drawn with two axes (X and Y axes), as shown in FIG. 15, the orbit of the actual motor draws a circle on the inner side of the real circle in accordance with the first degree delay time constant. The radius reduction .DELTA.R in this case is given as ##EQU2##
Here, R is the radius of the circle, and F is the speed in the tangential direction. Conventionally, feed forward control as shown in FIG. 16 is used to compensate for the radius error .DELTA.R which is generated due to the delay. By using this feed forward control, the radius reduction .DELTA.R is compensated for to ##EQU3##
By canceling the first degree delay having the first degree differential with the feed forward controller 7, and with the feed forward coefficient .alpha. set to 1, a motor orbit free from delay with respect to the command can be obtained.
Here, kp is a position loop gain, 1/kp is a time constant of the position loop, and S is a Laplace operator.
As other reference technical literature pertaining to the invention, there is "Acceleration and Deceleration Control System" disclosed in Japanese Patent Laid-Open No. 209812/85.
In the above feed forward control, however, the command is differentiated before being added. Therefore, command operation error is also differentiated, resulting in a waveform having many oscillating components. Consequently, by setting .alpha.=1, machine vibrations are liable to be induced. Therefore, it is difficult to provide total compensation of for .DELTA.R by using .alpha. above. Consequently, a smooth response waveform can not be obtained, resulting in vibrations of the machine.
Further, although the feed forward control is effective so far as the property of following commands, it has no suppression effect on external disturbances to the position feedback system. To enhance the suppression effect on external disturbances to the position feedback system, it is necessary to provide a high position loop gain kp. Doing so, however, leads to increased motor speed changes as in the torque waveform shown in FIG. 14B. Consequently, increased shocks are given to the machine, and also the tendency of picking up high frequency components (such as resonance of the machine system and noise) is increased. For the above reasons, stable gain increase can not be obtained.
FIGS. 17A and 17B show graphs for a comparison between the gain increase provided by a first order system and that provided by the high-order system according to the present invention. In gain increase with a conventional type of first order system, when a band required for control is raised, the system becomes like that shown with a dotted line in FIG. 17A. Also, a disturbance component becomes adapted to gain increase, so it comes to vibrate more easily. Namely, in a conventional type of first-order lag system, a band is attenuated by-20 dB. For this reason, when the gain is increased, a higher band width is required. However, the gain of the high frequency component also becomes higher, and the system is disadvantageously affected by a high-frequency noise more easily.